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Three-mode parametric interactions occur in triply-resonant optomechanical systems: photons from an optical pump mode are coherently scattered to a high-order mode by mechanical motion of the cavity mirrors, and these modes resonantly interact via radiation pressure force when certain conditions are met. Such effects are predicted to occur in long baseline advanced gravitational-wave detectors. They can pump energy into acoustic modes, leading to parametric instability, but they can also extract acoustic energy, leading to optomechanical cooling. We develop a large amplitude model of three-mode interactions that explains the ring-up amplitude saturation after instability occurs. We also demonstrate both radiation-pressure cooling and mechanical amplification in two different three-mode optomechanical systems, including the first observation of the three-mode parametric instability in a free-space Fabry-Perot cavity. The experimental data agrees well with the theoretical model. Contrary to expectations, parametric instability does not lead to loss of cavity lock, a fact which may make it easier to implement control techniques to overcome instability., Comment: 11 pages, 14 figures

We demonstrate the analogue of electromagnetically induced transparency in a room temperature cavity optomechanics setup formed by a thin semitransparent membrane within a Fabry-P\'erot cavity. Due to destructive interference, a weak probe field is completely reflected by the cavity when the pump beam is resonant with the motional red sideband of the cavity. Under this condition we infer a significant slowing down of light of hundreds of microseconds, which is easily tuned by shifting the membrane along the cavity axis. We also observe the associated phenomenon of electromagnetically induced amplification which occurs due to constructive interference when the pump is resonant with the blue sideband., Comment: 5 pages, 4 figures

We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of a thin semitransparent membrane placed within a high-finesse optical cavity. We study how the radiation pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor 350 We have also observed the mechanical frequency shift associated with the quadratic term in the expansion of the cavity mode frequency versus the effective membrane position, which is typically negligible in other cavity optomechanical devices., Comment: 15 pages, 7 figures

We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation treatment of the cavity eigenmodes., Comment: 10 pages, 6 figures